On lower confidence bound improvement matrix-based approaches for multiobjective Bayesian optimization and its applications to thin-walled structures

Abstract In engineering practice, most design criteria require time-consuming functional evaluation. To tackle such design problems, multiobjective Bayesian optimization has been widely applied to generation of optimal Pareto solutions. However, improvement function-based expected improvement (EI) and the hypervolume improvement-based lower confidence bound (LCB) infill-criteria are frequently criticized for their high computational cost. To address this issue, this study proposes a novel approach for developing multiobjective LCB criteria on the basis of LCB improvement matrix. Specifically, three cheap yet efficient infill-criteria are suggested by introducing three different improvement functions (namely, hypervolume improvement, Euclidean distance and maximin distance) that assemble the improvement matrix to a scalar value, which is then maximized for adding solution points sequentially. All these criteria have closed-form expressions and can maintain the anticipated properties, thereby largely reducing computational efforts without either integration or expensive evaluation of hypervolume indicator. The efficiency of the proposed criteria is demonstrated through the ZDT and DTLZ tests with different numbers of design variables and different complexities of objectives. The testing results exhibit that the proposed criteria have faster convergence, and enable to generate satisfactory Pareto front with fairly low computational cost compared with other conventional criteria. Finally, the best performing criterion is further applied to real-life design problems of tailor rolled blank (TRB) thin-walled structures under impact loads, which demonstrates a strong search capability for with good distribution of Pareto points, potentially providing an effective means to engineering design with strong nonlinearity and sophistication.